Question

The product of the ages of Alan and Terry is 80 more than the product of their ages 4 years prior. If Alan is 4 years older than Terry, what are their current ages?

Answer 1

Let

x ----> current Alan's age

y ----> current Terry's age

we have that

(x)(y)=(x-4)(y-4)+80 -----> equation 1

x=y+4 -----> equation 2

Solve the system of equations

substitute equation 2 in equation 1

(y+4)(y)=(y+4-4)(y-4)+80

solve for y

y^2+4y=y^2-4y+80

Simplify

4y+4y=80

8y=80

y=10

Find out the value of x

x=y+4 -----> x=10+4=14

therefore

Alan's age is 14 years old

Terry's age is 10 years old